Problem: Simplify. Multiply and remove all perfect squares from inside the square roots. Assume $x$ is positive. $2\sqrt{7x}\cdot 3\sqrt{14x^2}=$
Let's start by multiplying the factors within and without the square roots: $\begin{aligned} 2\sqrt{7x}\cdot 3\sqrt{14x^2}&=2\cdot 3\cdot\sqrt{7x}\cdot\sqrt{14x^2} \\\\ &=6\sqrt{98x^3} \end{aligned}$ Now we remove all perfect squares from inside the square root: $\begin{aligned} 6\sqrt{98x^3}&=6\sqrt{7^2\cdot x^2\cdot 2x} \\\\ &=6\sqrt{7^2}\cdot\sqrt{x^2}\cdot\sqrt{2x} \\\\ &=6\cdot 7\cdot x\sqrt{2x} \\\\ &=42x\sqrt{2x} \end{aligned}$ In conclusion, $2\sqrt{7x}\cdot 3\sqrt{14x^2}=42x\sqrt{2x}$